Characteristically simple group

In mathematics, in the field of group theory, a group is said to be characteristically simple if it has no proper nontrivial characteristic subgroups. Characteristically simple groups are sometimes also termed elementary groups. Characteristically simple is a weaker condition than being a simple group, as simple groups must not have any proper nontrivial normal subgroups, which include characteristic subgroups.

单词	Minimal normal subgroup
释义	Minimal normal subgroup 英语百科 Characteristically simple group In mathematics, in the field of group theory, a group is said to be characteristically simple if it has no proper nontrivial characteristic subgroups. Characteristically simple groups are sometimes also termed elementary groups. Characteristically simple is a weaker condition than being a simple group, as simple groups must not have any proper nontrivial normal subgroups, which include characteristic subgroups.
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Minimal normal subgroup

Characteristically simple group